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Publication Date:
February 2010
ISSN:
1435-5345
DOI:
10.1515/crelle.2010.037

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Journal für die reine und angewandte Mathematik

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The value distribution of additive arithmetic functions on a line

P. D. T. A. Elliott1

1Department of Mathematics, University of Colorado, Boulder, Colorado USA. e-mail: pdtae@euclid.colorado.edu

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2010, Issue 642, Pages 57–108, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2010.037, February 2010

Publication History:
Received:
2007-04-10
Revised:
2008-12-17
Published Online:
2010-02-09

Abstract

A stability study of the correlations of multiplicative arithmetic functions yields necessary and sufficient conditions that the frequency distributions naturally attached to sums of additive arithmetic functions ƒ1(n) + ƒ2(N – n) on the integers not exceeding N possess a limiting distribution as N traverses the positive integers, or the positive primes. Moreover, the functions ƒj may be allowed a wide class of unbounded renormalizations.

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